Editing Number (section)

===Zero{{anchor|History of zero}}===
{{refimprove section|date=November 2022}}
The first known recorded use of [[zero]] dates to AD 628, and appeared in the ''[[Brāhmasphuṭasiddhānta]]'', the main work of the [[Indian mathematician]] [[Brahmagupta]]. He treated&nbsp;0 as a number and discussed operations involving it, including [[division by zero]]. By this time (the 7th&nbsp;century), the concept had clearly reached Cambodia in the form of [[Khmer numerals]],<ref>{{Cite magazine |last=Aczel |first=Amir D. |date=2015-05-07 |title=My Quest to Find the First Zero |url=https://time.com/3845786/my-quest-to-find-the-first-zero/ |access-date=2025-02-15 |magazine=TIME |language=en}}</ref> and documentation shows the idea later spreading to China and the [[Islamic world]].

[[File:Khmer Numerals - 605 from the Sambor inscriptions.jpg|thumb|The number 605 in [[Khmer numerals]], from an inscription from 683 AD. Early use of zero as a decimal figure.]]

Brahmagupta's ''Brāhmasphuṭasiddhānta'' is the first book that mentions zero as a number, hence Brahmagupta is usually considered the first to formulate the concept of zero. He gave rules of using zero with negative and positive numbers, such as "zero plus a positive number is a positive number, and a negative number plus zero is the negative number". The ''Brāhmasphuṭasiddhānta'' is the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit in representing another number as was done by the Babylonians or as a symbol for a lack of quantity as was done by Ptolemy and the Romans.

The use of 0 as a number should be distinguished from its use as a placeholder numeral in [[place-value system]]s. Many ancient texts used&nbsp;0. Babylonian and Egyptian texts used it. Egyptians used the word ''nfr'' to denote zero&nbsp;balance in [[double-entry bookkeeping system|double entry accounting]]. Indian texts used a [[Sanskrit]] word {{lang|sa-Latn|Shunye}} or {{lang|sa|shunya}} to refer to the concept of ''void''. In mathematics texts this word often refers to the number zero.<ref>{{cite web |url=http://sunsite.utk.edu/math_archives/.http/hypermail/historia/apr99/0197.html |title=Historia Matematica Mailing List Archive: Re: [HM] The Zero Story: a question |publisher=Sunsite.utk.edu |date=1999-04-26 |access-date=2012-01-30 |url-status=dead |archive-url=https://web.archive.org/web/20120112073735/http://sunsite.utk.edu/math_archives/.http/hypermail/historia/apr99/0197.html |archive-date=2012-01-12 }}</ref> In a similar vein, [[Pāṇini]] (5th century BC) used the null (zero) operator in the ''[[Ashtadhyayi]]'', an early example of an [[formal grammar|algebraic grammar]] for the Sanskrit language (also see [[Pingala]]).

There are other uses of zero before Brahmagupta, though the documentation is not as complete as it is in the ''Brāhmasphuṭasiddhānta''.

Records show that the Ancient Greeks seemed unsure about the status of&nbsp;0 as a number: they asked themselves "How can 'nothing' be something?" leading to interesting [[philosophical]] and, by the Medieval period, religious arguments about the nature and existence of&nbsp;0 and the vacuum. The [[Zeno's paradoxes|paradoxes]] of [[Zeno of Elea]] depend in part on the uncertain interpretation of&nbsp;0. (The ancient Greeks even questioned whether&nbsp;{{num|1}} was a number.)

The late [[Olmec]] people of south-central Mexico began to use a symbol for zero, a shell [[glyph]], in the New World, possibly by the {{nowrap|4th century BC}} but certainly by 40&nbsp;BC, which became an integral part of [[Maya numerals]] and the [[Maya calendar]]. Maya arithmetic used base&nbsp;4 and base&nbsp;5 written as base&nbsp;20. [[George I. Sánchez]] in 1961 reported a base&nbsp;4, base&nbsp;5 "finger" abacus.<ref>{{Cite book |last=Sánchez |first=George I. |author-link=George I. Sánchez |title=Arithmetic in Maya |publisher=self published |year=1961 |place=Austin, Texas}}</ref>{{Better source needed|reason=The only source is a self-published book, albeit one by a respected educator. According to the (favorable) review by David H. Kelley in 'American Anthropologist', Sánchez was neither a Mayanist nor a mathematician. The review does not mention the abacus.|date=September 2020}}

By 130 AD, [[Ptolemy]], influenced by [[Hipparchus]] and the Babylonians, was using a symbol for&nbsp;0 (a small circle with a long overbar) within a [[sexagesimal]] numeral system otherwise using alphabetic [[Greek numerals]]. Because it was used alone, not as just a placeholder, this [[Greek numerals#Hellenistic zero|Hellenistic zero]] was the first ''documented'' use of a true zero in the Old World. In later [[Byzantine Empire|Byzantine]] manuscripts of his ''Syntaxis Mathematica'' (''Almagest''), the Hellenistic zero had morphed into the Greek letter [[Omicron]] (otherwise meaning&nbsp;70).

Another true zero was used in tables alongside [[Roman numerals#Zero|Roman numerals]] by 525 (first known use by [[Dionysius Exiguus]]), but as a word, {{lang|la|nulla}} meaning ''nothing'', not as a symbol. When division produced&nbsp;0 as a remainder, {{lang|la|nihil}}, also meaning ''nothing'', was used. These medieval zeros were used by all future medieval [[computus|computists]] (calculators of Easter). An isolated use of their initial, N, was used in a table of Roman numerals by [[Bede]] or a colleague about 725, a true zero symbol.